Details:
Title  An alternative approach to comprehensive Gröbner bases  Author(s)  Yosuke Sato, Akira Suzuki  Type  Article in Journal  Abstract  We give an alternative definition of comprehensive Gröbner bases in terms of Gröbner bases in polynomial rings over commutative Von Neumann regular rings. Our comprehensive Gröbner bases are defined as Gröbner bases in polynomial rings over certain commutative Von Neumann regular rings, hence they have two important properties which do not hold in standard comprehensive Gröbner bases. One is that they have canonical forms in a natural way. Another one is that we can define monomial reductions which are compatible with any instantiation. Our comprehensive Gröbner bases are wider than Weispfenning’s original comprehensive Gröbner bases. That is there exists a polynomial ideal generated by our comprehensive Gröbner basis which cannot be generated by any of Weispfenning’s original comprehensive Gröbner bases.  Keywords  Gröbner basis  Length  19  ISSN  07477171 
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 URL 
dx.doi.org/10.1016/S07477171(03)000981 
Language  English  Journal  Journal of Symbolic Computation  Series  ISSAC 2002  Volume  36  Number  34  Pages  649667  Publisher  Academic Press, Inc.  Address  Duluth, MN, USA  Year  2003  Edition  0  Translation 
No  Refereed 
No 
